自适应多重网格法与超松弛法的比较

多重网格法(Multiple Grid Method,简称M-G方法)是近年来出现的快速方法之一,本文在M-G方法中采用自适应控制层间转换的技术,并将自适应M-G方法与G-S迭代方法及SOR迭代方,法进行了比较。其计算结果表明,自适应M-G方法的计算量比G-S迭代及SOR迭代少得多,当M-G方法所用层数为4-6层,这种优越性就更加明显,且自适应M-G方法中选取控制参数有很大的灵活性。

The Comparision between Adaptive Multiple Grid Method and Successive Overrelaxation Method

In this paper, adaptive multiple grid method (it is called adaptive MG method) is used to solve linear elliptic equations.The metliod is compared with GS method and SOR method, the practical computations have indicated following results:1. The convergence rate and computation time of adaptive, MG method are fewer than GS method and SOR method, so adaptive MG method is a fast, method,2. When mesh layers are many, up to six layers, the more the number of layer ,using for adaptiveMG method is, the higher computational efficiency is.3. In the determinate range, we can use freely controlling parameters which control interaction's transform between coarse grids and fine -grids, they have not large influce to computation work. But, the choice of a approximate optimum relaxation factor of SOR method requires much experimenting or computational experience.